A $1 cm$ long string vibrates with fundamental frequency of $256\, Hz$. If the length is reduced to $\frac{1}{4}cm$ keeping the tension unaltered, the new fundamental frequency will be

Transverse waves of same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of velocities of wave in $A$ and $B$ is

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$.....$

The length of a son meter wire $AB$ is $110\; cm$. Where should the two bridges be placed from $A$ to divide the wire in $3$ segments whose fundamental frequencies are in the ratio of $1:2:3$?

A man can hear sounds in frequency range $120\,Hz$ to $12020\,Hz$. only. He is vibrating a piano string having a tension of $240\,N$ and mass of $3\,gm$ . The string has a length of $8\,m$ . How many different frequencies can he hear ?

The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-